This book is devoted to the mathematical foundation of boundary integral equations. The combination of finite element analysis on the boundary with these equations has led to very efficient computational tools, the boundary element methods (see e. g., the authors [139] and Schanz and Steinbach (eds.) [267]). Although we do not deal with the boundary element discretizations in this book, the material presented here gives the mathematical foundation of these methods. In order to avoid over generalization we have confined ourselves to the treatment of elliptic boundary value problems.